Why is there no single slit interference when one slit is closed in a double slit experiment?

[PeterDonis]

I think, I cannot prove it, that the behavior of photons/electrons in the double slit experiment will ultimately turn out to be classical.

We already know this is not the case: neither classical particle theory nor classical wave theory can explain all of the experimentally observed behavior.

 

[elou]

It's been published many times over the past two and half centuries (not by me of course) and you'll find it in any textbook treatment of waves. Crawford's "Waves" is volume 3 of the Berkeley Physics series, a standard textbook for the third semester of a undergraduate physics program and a good starting point - I'm partial to it because it's the one my professor used so I have a copy on my bookshelf.

But, repeating myself, this is not quantum mechanics. It is classical wave behavior and a prerequisite to quantum mechanics (which started for me in the fourth semester). The quantum mechanical double slit experiment works more like:

The probability of a photon landing at any given point on the screen is calculated by considering all possible paths between the photon source and that point. Each path makes either a positive or a negative contribution to that probability, and we sum all of these to get the total probability (the actual probability is the square of this sum).
When two slits are open a photon can pass through either slit. There will be some areas of the screen where the contribution from paths through one slit will be positive while that from the other is negative and they cancel; in others both will have the same sign and they reinforce one another; and we get the alternating regions of high and low probability that make an interference pattern after enough photons have made their dots on the screen.

But when we close a one slit, or place a detector at a slit, then any given photon can only have gone through one slit or the other, so we only have the contributions from the path through that one slit. There’s no opposite sign contribution from the other slit to cancel or reinforce it, so no interference pattern. There still is a bit of pattern, usually called a “diffraction pattern”, that comes from having some paths through the left-hand side of the single slit and others through the right-hand side.

The connection to classical electromagnetic waves, Young's double-slit experiment, and other "let's make an interference pattern with laser light" demonstrations is that the probability amplitudes in the quantum mechanical experiments obey a wave equation similar to the classical wave equation. Thus we need the mathematical techniques of Crawford's book or equivalent before we can start in on the quantum mechanical problem, and we can use our intuition from the classical waves as an analogy to get a feel for how the quantum mechanical probabilities behave. And if we're trying for a layman-friendly math-free explanation, that analogy is all we have.... but it leads to confusion when people hear it, mistake the analogy for the real thing, and come away believing that Young and subsequent optical demonstrations are showing quantum mechanical behavior.

Feynman’s non-serious layman-friendly book “QED: The strange theory of light and matter” is worth reading. It is no substitute for learning the math, but it goes into more interesting examples of this “contributions from all paths” model.

I am assuming you are correct in your analysis, and that is exactly what I do not understand. Whether one uses the math-friendly approach, or the strict one, if I understand you correctly, we can state that:
"
But when we close a one slit, or place a detector at a slit, then any given photon can only have gone through one slit or the other, so we only have the contributions from the path through that one slit. There’s no opposite sign contribution from the other slit to cancel or reinforce it, so no interference pattern. There still is a bit of pattern, usually called a “diffraction pattern”, that comes from having some paths through the left-hand side of the single slit and others through the right-hand side."

And that is my problem right there. I don't care, for this question, what the interpretations are. What interests me is what happens when one slit is closed. I do not understand why we then do not see a more or less similar pattern of interference, as we see with the single slit. Are there objective reasons for that?

 

[Drakkith]

What interests me is what happens when one slit is closed. I do not understand why we then do not see a more or less similar pattern of interference, as we see with the single slit. Are there objective reasons for that?

Do you understand the classical treatment of this experiment?

 

[renormalize]

What interests me is what happens when one slit is closed. I do not understand why we then do not see a more or less similar pattern of interference, as we see with the single slit. Are there objective reasons for that?

The math of Huygens Principle is the objective reason.

(https://physicscourses.colorado.edu/phys2020/phys2020LabMan2000/2020labhtml/Lab5html/lab5.html)
A single slit of width $D$ produces the broad diffraction pattern shown in dashes. Two similar slits spaced $d>D$ apart produce narrow interference fringes whose overall amplitude is modulated by the single slit diffraction patterns.

 

[PeroK]

What interests me is what happens when one slit is closed. I do not understand why we then do not see a more or less similar pattern of interference, as we see with the single slit.

Why not find a source that shows the experiment itself? Rather than someone talking about the theory. Either there is single slit diffraction or there is not. You need a real experiment to confirm the case.

 

[PeroK]

Here, for example.

 

[PeroK]

I must confess I'm intrigued by the psychology of the popular science presenters in this case. The above video presents a real experiment presented simply and demonstrates the real physics. Just some random guy on the Internet - although he is a professor of physics!

The Royal Institution, on the other hand, commisions a well-known TV physicist to present the physics to a wider audience. And, we get something quite different. A misleading or even incorrect version of the physics, where there is no single-slit diffraction. Instead, light behaves like a classical particle and does not diffract. Yet, when both slits are open it behaves like a wave, diffracts at both slits and subsequently produces interference.

PS in that RI video, al-Khalili states explicitly that when one slit is open the atom passing through the slit acts like a particle; but, when both slits are open it acts like a wave! Which is extraordinarily wrong!

 

[elou]

and still, nobody is answering my question.
If it was a matter of different width in each case then there would not be any problem. And I am sure that would already have been pointed out.
So why don't you guys admit that this is yet another unexplained aspect of light, and let's close this subject?

 

[WernerQH]

It appears that nobody really understands your question, and the sharp distinction between the words diffraction and interference that you seem to make. Do you understand the classical description of these experiments? Classically there is but one formalism that describes the diffraction/interference patterns for all possible geometries (single or double slit, gratings, ...). But different geometries means a different experiments.

 

[PeroK]

and still, nobody is answering my question.

What question?

 

[PeroK]

So why don't you guys admit that this is yet another unexplained aspect of light, and let's close this subject?

You mean that a narrow single slit causes diffraction. But, if there are two narrow slits and you close one, there is no diffraction?

 

[weirdoguy]

So why don't you guys admit that this is yet another unexplained aspect of light

Because it's explained. I don't really think you are reading what everyone is saying. Are you trolling?

 

[sophiecentaur]

Are there objective reasons for that?

and still, nobody is answering my question.

So why don't you guys admit that this is yet another unexplained aspect of light

It is clearly not explainable in your terms and that is your problem. You cannot demand an 'explanation' that takes care of your particular intuitive model. All the models we hold in our heads are just models; they do not dictate what is the truth. They are just models that help with out predictions about measurements.

It's definitely worth while approaching this in terms of classical wave theory first and come to terms with the fact that EM waves have no effect on each other (superposition in a linear medium). An observer, at some position, will measure the vector sum of two passing waves. This vector sum can produce all resultants between addition and subtraction (sometimes cancellation), according to where you observe. In the two slit experiment, you get the well known interference pattern. But each wave has no idea about the presence of the other wave (well, it wouldn't, would it?); the pattern is visible only because the screen responds in some way to both waves.

If you can accept / understand the maths of wave interference then the above will show how an interference pattern can be formed (and, by extension, the formation of diffraction patterns). If you can't do that then you are not in a position to argue against (or even claim to understand) any further steps. I am not being stroppy here - it's just the way it is; you need to know about vectors and trigonometry.

The grains of sand idea (al-Khalili 's video) doesn't work for particles like electrons (or photons, of course). This fact indicates that all these particles must behave in a wavelike way. They 'appear to' elbow each other aside in some directions (the nulls) but it is perfectly (and experimentally) consistent.

None of this is "unexpected" if you follow it all through properly. If you want to go out on a limb with your own version of things (by rejecting the accepted system) then you have to replace the whole of Physics in a self consistent model. Keep at it and you will see the system makes sense.

 

[elou]

It is clearly not explainable in your terms and that is your problem. You cannot demand an 'explanation' that takes care of your particular intuitive model. All the models we hold in our heads are just models; they do not dictate what is the truth. They are just models that help with out predictions about measurements.

It's definitely worth while approaching this in terms of classical wave theory first and come to terms with the fact that EM waves have no effect on each other (superposition in a linear medium). An observer, at some position, will measure the vector sum of two passing waves. This vector sum can produce all resultants between addition and subtraction (sometimes cancellation), according to where you observe. In the two slit experiment, you get the well known interference pattern. But each wave has no idea about the presence of the other wave (well, it wouldn't, would it?); the pattern is visible only because the screen responds in some way to both waves.

If you can accept / understand the maths of wave interference then the above will show how an interference pattern can be formed (and, by extension, the formation of diffraction patterns). If you can't do that then you are not in a position to argue against (or even claim to understand) any further steps. I am not being stroppy here - it's just the way it is; you need to know about vectors and trigonometry.

The grains of sand idea (al-Khalili 's video) doesn't work for particles like electrons (or photons, of course). This fact indicates that all these particles must behave in a wavelike way. They 'appear to' elbow each other aside in some directions (the nulls) but it is perfectly (and experimentally) consistent.

None of this is "unexpected" if you follow it all through properly. If you want to go out on a limb with your own version of things (by rejecting the accepted system) then you have to replace the whole of Physics in a self consistent model. Keep at it and you will see the system makes sense.

You are giving too much credit to Quantum theory, a credit it neither deserves nor asks for, except maybe in its most extreme interpretations. QM is capable of calculating probabilities, nothing more. It is its raison d'être. In fact Heisenberg goes so far as to say that QM cannot go further than that, because that is how nature is. Other interpretations attempt to mitigate this view of reality by, among other things, imagining multiple universes. But at the end of the day, when it come to this universe, they all admit they simply do not know.
That makes it very strange to hear from people that I just have to do the math and everything would then become clear.

edit: what I apparently fail to convey is this simple idea: whatever the reason, in a double slit experiment, we see something which is very similar to what we see when we use a single slit the same way. When we close one of the two slits, the second slit does not show what the first single slit did. I find it strange, and wonder how that comes. I am interested in any explanation that makes sense within the view presented. I do not have to agree with the view, but if the explanation is consistent with it, then I am satisfied.

 

[gentzen]

I find it strange, and wonder how that comes. I am interested in any explanation that makes sense within the view presented. I do not have to agree with the view, but

I would often try and offer explanations and images which could make sense for people who have trouble with an "just have to do the math" answer. But the way you acted here suggests to me that I would not do myself a favor in your case:

You should publish your view. I am sure it will receive a lot of attention, because

So you are accusing Nugatory of inventing his own new views.

I think, I cannot prove it, that the behavior of photons/electrons in the double slit experiment will ultimately turn out to be classical.

And then follow-up with the conviction that there would be a classical explanation for quantum behavior.

In fact Heisenberg goes so far as to say that QM cannot go further than that, because that is how nature is.

Bashing Heisenberg for things he never did nor say does not leave a good impression with me either.

 

[PeroK]

edit: what I apparently fail to convey is this simple idea: whatever the reason, in a double slit experiment, we see something which is very similar to what we see when we use a single slit the same way. When we close one of the two slits, the second slit does not show what the first single slit did. I find it strange, and wonder how that comes. I am interested in any explanation that makes sense within the view presented. I do not have to agree with the view, but if the explanation is consistent with it, then I am satisfied.

As others have pointed out, that is classical wave behaviour. Single slit diffraction and double-slit interference. There is no mystery there.

QM only enters the picture because those phenomena are also observed using electrons, which were thought to be classical particles.

QM is also needed to explain those phenomena for very low intensity light (down to one photon at a time), where the classical wave explanation breaks down somewhat.

 

[PeroK]

PS note that your belief that single slit diffraction doesn't occur if there are two slits and one is closed is a delusion. Which could be dispelled if you had the capability to carry out the experiment yourself.

 

[Nugatory]

What interests me is what happens when one slit is closed. I do not understand why we then do not see a more or less similar pattern of interference, as we see with the single slit.

If I am understanding you properly, you are asking “Why does two slits with one closed not produce the same pattern as one slit?”
If that is the question, it was answered by BvU in #2 of this thread: Two slits with one closed produces the same pattern as one slit so there is nothing to explain.

 

[elou]

PS note that your belief that single slit diffraction doesn't occur if there are two slits and one is closed is a delusion. Which could be dispelled if you had the capability to carry out the experiment yourself.

If that is the case, then you are absolutely right. I honestly have difficulty believing the purist interpretation that is dominating this discussion. I have read many articles on the subject that are considered as "reputable" and peer-reviewed, and I have never met an interpretation like the one expressed here.
Please believe me when I say that I have no problem with this interpretation. One of the many questions that I have on the subject, is whether what we see on video clips, and is also presented in serious articles, is not a result of the different magnification level so-called interference patterns are viewed. After all, we are talking about microscopic phenomena, and each level of magnification will reveal its own details. I have asked this question one to a YouTube presenter [yes, I know!] and never got a response either.

 

[Nugatory]

I have read many articles on the subject that are considered as "reputable" and peer-reviewed

You have not, however, referenced any of these. You have referenced only misleading and oversimplified popularizations.

One of the many questions that I have on the subject, is whether what we see on video clips, and is also presented in serious articles, is not a result of the different magnification level so-called interference patterns are viewed. After all, we are talking about microscopic phenomena, and each level of magnification will reveal its own details.

Please take a moment to review the forum rules about personal speculations.

I have asked this question one to a YouTube presenter [yes, I know!] and never got a response either.

You can spend years asking questions of YouTube presenters, studying pop-sci videos and online sources, and when you're done you won't know or understand quantum mechanics any better than when you started. There really is no substitute for a decent undergraduate textbook.

The question you asked in the initial post and your followup questions have been answered so this thread is closed.

 

[PeterDonis]

What interests me is what happens when one slit is closed. I do not understand why we then do not see a more or less similar pattern of interference, as we see with the single slit.

Just to clarify: multiple people in this thread told you that, in the single slit case, we do see a diffraction pattern (what you are calling a "single slit interference pattern", although that is a bad term for it). The pop science sources you are using are simply glossing over that fact. Better sources, such as textbooks and peer-reviewed papers, will not.